Blend mode to achieve "Glow" effect with texture painting from Image Editor (No Compositor)
That result you show is not from a simple blend mode in photoshop, that is from a specific set of steps to render that effect.
To replicate, it is the same process first that you have in photoshop when painting into an image or layer of 0 alpha - you have to first paint pixels into the image/layer to be able to have affect them with subsequent blend mode actions. Paint your shape first with your brush set to Mix mode, and if need be use a low strength brush. Set your blend mode to Add and turn on pressure sensitivity, then paint carefully at center with your brush radius encompassing all of your available pixels. Reduce radius and repeat in center of the shape. Soft Light blend mode can also help a little, depending on what color you use to react to the original pixels. Don't forget to also see if using the Blur or Smear tools can help here as well depending on your desired output.
Main take away you need to understand is that you can't make pixels 'glow' if they aren't pixels of solid color yet. Photoshop and all other image editors like Blender also work this way with painting tools.